New approach to robust L₂-L_∞ filter design for uncertain continuous-time systems

With the help of Projection Lemma, a new L₂-L_∞ performance criterion is derived, which exhibits a kind of decoupling between Lyapunov matrix and system matrices. This kind of decoupling is enabled by introduction of an additional slack variable and enables us to obtain a parameter-dependent Lyapunov function for polytopic uncertain systems. Upon the proposed performance condition and by means of linear matrix inequality technique, both full-order and reduced-order robust L₂-L_∞ filtering problems are solved in a unified framework. The proposed approach can be further extended to deal with filtering problems with pole constraint. Compared with earlier result in the quadratic framework, our approach turns out to be less conservative.